Penalized optimal scaling for ordinal variables with an application to international classification of functioning core sets

Author:

Hoshiyar Aisouda1ORCID,Kiers Henk A. L.2,Gertheiss Jan13

Affiliation:

1. School of Economics and Social Sciences Helmut Schmidt University Hamburg Germany

2. Faculty of Behavioural and Social Sciences University of Groningen Groningen The Netherlands

3. Department of Biostatistics, Epidemiology and Informatics University of Pennsylvania Philadelphia Pennsylvania USA

Abstract

AbstractOrdinal data occur frequently in the social sciences. When applying principal component analysis (PCA), however, those data are often treated as numeric, implying linear relationships between the variables at hand; alternatively, non‐linear PCA is applied where the obtained quantifications are sometimes hard to interpret. Non‐linear PCA for categorical data, also called optimal scoring/scaling, constructs new variables by assigning numerical values to categories such that the proportion of variance in those new variables that is explained by a predefined number of principal components (PCs) is maximized. We propose a penalized version of non‐linear PCA for ordinal variables that is a smoothed intermediate between standard PCA on category labels and non‐linear PCA as used so far. The new approach is by no means limited to monotonic effects and offers both better interpretability of the non‐linear transformation of the category labels and better performance on validation data than unpenalized non‐linear PCA and/or standard linear PCA. In particular, an application of penalized optimal scaling to ordinal data as given with the International Classification of Functioning, Disability and Health (ICF) is provided.

Funder

Deutsche Forschungsgemeinschaft

Publisher

Wiley

Subject

General Psychology,Arts and Humanities (miscellaneous),General Medicine,Statistics and Probability

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